history of geometry

In this blog we will learn about history of geometry,

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers.History of geometry goes way back into the centuries.

Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.Next we will learn about 4 grade math, The topics involved in four grade math are number sense, patterns, addition, measurement, subtraction, multiplication, functions, fractions & mixed numbers, division, algebra, decimals, adding and subtraction of decimals and probability & statistics. In this article we shall discuss about the example problems involved in four grade math.In the next blog we will learn about fraction simplifier.Hope you like the above example of history of geometry,please leave your comments if you have any doubts.

multiplying monomials

In this blog we will learn about multiplying monomials,again we can understand this with the help of an example.

Problem 1 for multiplying monomial:

(x³) (x⁴)

= x³⁺⁴

= x⁷

Problem 2 for multiplying monomial:

(x² y) ( x³ y ²)

= (x². x³) ( y . y²)

= x²⁺³ . y¹⁺²

= x⁵y³

Problem 3 for multiplying monomials:

( 6k⁵ ) ( 5k² )

= ( 30 k⁷) ( multiply numbers )

Problem 4 for multiplying monomial:

-4 ( m² n ) ( -3 m⁴ n³ )

= ( -4 . -3 ) ( m² . m⁴ ) ( n . n³ )

= ( 12 ) ( m²⁺⁴ ) ( n¹⁺³ )

= 12 m⁶ n^4.

^{Next we will learn about angle bisector theorem. An angle bisector is a portion tense from any peak of a polygon that cuts that weight into two rival angles. In all the trigon, the trey angles bisectors instrument meet at a singular quantity inside the triangle. If the bisector of the extremum standpoint of an Isosceles polygon is haggard, then the bisector is right to the part of the trilateral. Here we are accomplishment to see and confirm search bisector theorem.In the next blog we will learn about types of lines.Hope you like the above example of multiplying monomials,please leave your comments if you have any doubts.}

4th grade math problems

In this blog we will learn about 4th grade math problems,let us now look at few examples of 4th grade math problems, 4th grade math problems mainly cover addition, subtraction, multiplication, and division problems

1) Solve, 3(4+3) – 9 + 3(4)

Solution:
= 3(7) – 9 + 12
= 21 + 3
= 24

2) Solve, 5 + * 5 + 5

Solution:
= 5 + 2 * 5 + 5
= 5 + 10 + 5
= 20

3) Solve, 6² + 7²

Solution:

= (6 * 6) + (7 * 7)
= 36 + 49
= 85.

Next let us learn about four sided shapes,

Any four sided shape is called as quadrilateral . the following are the examples for four sided shapes, they are

1. Square

2. Rectangle.

3. Rhombus.

4. Parallelogram.In the next blog we will learn about percentage change calculator.Hope you like the above example of 4th grade math problems,please leave your comments if you have any doubts.

calculating ratios

In this blog let us learn about calculating ratios,in arithmetic, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of one quantities indicates how plenty of times the first quantity is contained in the second & may be expressed algebraically as their quotient.We can get a clear picture about calculating ratios with the help of an example problem of a inverse ratio,

Ex 2:

Solve

Sol:

=

= (numerator and denominator are divided by 10)

=

Answer is 2 by 3 or 2:3.

In the next Blog we will learn about algebra rules and also about geometry calculator,hope you like the above example of calculating ratios,please leave your comments if you have any doubts.

find percentage

In this blog we will learn how to find percentage,we can learn about this with the help of an example problem,Find the percentage of math students out of 50 students if only 34 are from mathematics department.
Given that
Total number of students = 50
Math students = 34
Percentage of math students = (34/50) x 100
= 34 x 2
= 68
There are 68% of math students.This is one of the methods to Find the percentage of math students out of 50 students if only 34 are from mathematics department.
Given that
Total number of students = 50
Math students = 34
Percentage of math students = (34/50) x 100
= 34 x 2
= 68
There are 68% of math students.This is one of the methods to find percentage,next we will learn about elementary statistics,in statistics, the mean, median, range, and mode these are very important and very simple terms in the elementary statistics.In the next blog we will learn about geometric formulas.
Hope you like the ab0ve example of find percentage,please leave your comments if you have any doubts.

what is differentiation

In this blog let us learn about what is differentiation,Differentiation means discriminating any two things into different and distinct and define as the rate of change of a function with respect to one of its variable.Definition of simple differentiation.Simple differentiation defines as how a function changes with respect the other variable. Which is usually expressed as 'delta' change.Differentiation is known as the process to compute the rate at which a dependent output y changes with respect to the change in the independent input x.This pace of change is known as the derivative of y with respect to x. In lay mans terms the relying factor of y upon x means that y is a function of x.This functional relationship is often signified as y = ƒ(x), where ƒ denotes the function. If x and y are real numbers,and if the graph of y is marked against x, then derivative measures the slope of this graph at each point.If the student learns the various processes it helps them to learn how to write numbers,in the next blog we will learn about properties of multiplication,hope you like the above example of what is differentiation,please leave your comments if you have any doubts.

Using math logarithms

Welcome to math tutors online,
We need to talk about logarithms. Say you have 2^x = 64
(2^x is my way of saying "2 raised to the x power"), and you want to
solve for x.

Well, we know that
64 = 2*32 = 2*(2*16) = 2*2*2*8 = 2*2*2*2*2*2 = 2^6, so x = 6.

How about 2^x = 5? There we're stuck, because 2^2 = 4 and 2^3 = 8
so x should be somewhere between 2 and 3 to make 2^x = 5.

There's another way of saying what x should be, and this is called the
logarithm of 5 to the base 2. examples on free math; That is, x = log[2](5); (the 2 should be
a subscript, like a power but typed a bit below the log, so it isn't
log 10). In general, the solution to b^x = n for some given b and n is
x = log[b](n). b is called the *base* of the logarithm.
Learn more on online math tutors.

Engineering calculations

Greetings from math tutor online free,

Engineers really do carry out some of these types of calculations, but
the mathematics textbooks tend to simplify the problems quite a bit
(which is not necessarily a bad thing; examples on free math; this type of problem really
does illustrate how specific mathematical concepts are applied to
other fields.)

For engineers in the world, the support column
mentioned above might also need to hold 28 tons after it is eighty
years old, has been crashed into by three cars and a truck, and has
survived four earthquakes and one flood. Now how would you calculate
the diameter? By the way, don't forget that the concrete at the
bottom of the column also needs to hold the weight of the column
itself in addition to the 28 ton 'load'. learn more on math helper.

Math in applied science

Welcome to free math tutoring,

Actually, there are some common misconceptions about the use of mathematics in
the applied sciences, like engineering: most engineers actually spend
a very small portion of their time carrying out mathematical
calculation. But that does not mean that mathematics is not important
to engineering. In fact, mathematics is indispensable.

Let me expand my answer into four different areas, because I have
thought of four different ways in which civil engineers (and other
engineers) use mathematics. online math forum; I'm sure there are many others. These
are just the first four that come to mind:

1. To help them understand the chemistry and physics fundamental to
the construction of civil engineering projects;

2. To carry out the technical calculations necessary to plan a
construction project;

3. To help them with modeling and simulations to predict the
behavior of structures before they are actually built; and

4. To help them with business decisions and other 'non-technical'
aspects of their jobs.

Now let us study more on math forum.

Right Calculations

Welcome to free math help,
It's unfortunate that your teacher doesn't seem to
have a gift for making math come alive. On the other hand, this is an
opportunity for you to learn a very valuable lesson, which is that you
don't need to wait around for teachers to teach you math - or anything
else - in order for you to learn it.

My advice to you is to take charge of your own education in math. So,
how do you do that?

You'll never go wrong by starting at the beginning! I would suggest
starting with your present textbook and working through it. examples on math tutors online, Read each section, and work the problems for that section until they seem too
easy. Then go to the next section. more examples on math helper.

Learning Math

Welcome to free math tutoring,
you've been able to learn other
things easily because you've been able to instantly form lots of
connections to things that you already know. If you've worked with
wood a lot, then you already have a feel for much of what you'd learn
in a class on trigonometry.

If you've worked with pottery, or
sculpture, then you already have a feel for much of what you'd learn
in a class on integral calculus. free math ;That is, you'd be learning new
syntax, but you'd already have a handle on the semantics.

The best way
to understand _anything_ that you're told in a math class is to come
at it from the direction of something that you understand intuitively.
That way, each new pattern or formula isn't a new, isolated fact to be
memorized, but just a new way of looking at something you already
know.
more examples on online math forum.

Math Zonogon

Welcome to free math help,
The introduction of the idea of a zonogon (all pairs of opposite sides
parallel and congruent) looked as if it might make the term Calligram
superfluous until we found the hexagon created by lopping off the
corners of a regular triangle. math helper; Parallel opposite sides then did not
imply equal opposite sides, and the Calligram (or whatever someone
already named it) is preserved as a unique set.

Still, it surprises me, after reading the definitions for things like
'open', 'closed', 'bounded', etc. that 'opposite' wouldn't show up in
a glossary. Especially when you think of all the geometric theorems
that use the term - "the side opposite the largest angle in a
triangle..." etc. If a published formal definition pops up, please let
me know. learn more on online math forum.

Importance of Math

Welcome to free online math help,
One thing you're learning together is why mathematicians have to
define all their terms before they can state, and especially prove,
conjectures. If you can all agree on some definition of "opposite,"
that would work fine for your purposes. I don't see anything wrong
with my definition, free math; though it's probably one of those things that we
tend to assume we all understand.

Certainly your definition that
opposite means parallel makes your whole conjecture circular, and to
count a pentagon as fitting your definition when by your definition
any sides that aren't parallel simply don't have opposites seems
really odd.
more examples on math forum.

Geometry History

Welcome to math tutoring,

Let us study the History of Geometry on free math help,

look in the front of your textbook. Each
geometry course is organized a little differently, and the authors of
the book developed this particular course. But all geometry courses
more or less follow the trail blazed by Euclid, before 300 BC.

There were others who contributed to geometry centuries earlier in Greece,
and even farther back, the Babylonians and Egyptians had some practical
geometrical knowledge. But Euclid is the one who systematized geometry
- set it up as a collection of definitions, postulates, and theorems,
all logically following from one another.
Now let us study more on online math forum.

Math Arithmetic

Once, while I was still a child in school, I heard that
'minus times minus is plus'. How strange it seemed that
negatives could cancel out -- as though two wrongs could
make a right. math helper; I wondered if there could be something else,
still like arithmetic, but having yet another sign. Why
not make up some number things, I thought, that go not
just two ways, but three? I searched for days, making up
new little multiplication tables. Alas, each system ended
either with impossible arithmetic (e.g., with one and two
the same), with no signs at all, or with an extra sign.
Eventually, I gave up. If I had had the courage to persist,
as Gauss did, I might have discovered the arithmetic of
complex numbers, or, as Pauli did, the arithmetic of spin
matrices. But no one ever finds a three-signed imitation
of arithmetic because, it seems, it simply doesn't exist.

Try, for example free online math tutor, to make a new number system that's like the
ordinary one except that it skips some number -- say, 4. It
just won't work. Everything will go wrong. You'll have to
decide what 2 plus 2 is. If you say that this is 5, then 5
will have to be an even number, and so also must 7 and 9.
Then, what's 5 plus 5? Is it 8, or 9, or 10? You'll find that
to make the new system at all like arithmetic you'll have to
change the properties of all the other numbers. Then, when
you're done, you'll find that you have changed only those
numbers' names and not their properties at all. more examples on math forum.

Ancient Egyptian Numbers

Let us study free math Egyptian Numerical,

In 3000B.C the Egyptians had a numerical writing system based on hieroglyphs. Hieroglyphs are represented in the form of pictures. The Egyptians had a bases 10 system of hieroglyphs for numerals.

They standardized separate numerical symbols for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million.
I hope the above explanation was useful in this math forum, continue reading i'll help you with free online math tutoring.

Math Signs

Math Signs:Given below are some math signs that are used while solving the various math problems,these signs are also very helpful while getting math solutions,they make is easier to solve a problem and also to get the end result.Hope you like the above example of Math Signs,please leave your comments if you have any doubts.

What is pie in math

Let us learn what is pie in math: π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers.Now that we learnt and understood what is pie in math in the coming blogs we will learn what is a trapezoid.Hope you like the above example of pie.Please leave your comments if you have any doubts.

Proofs in Geometry

Proofs in Geometry:In this blog we will learn about Proofs in Geometry and about a polynomial function,a polynomial function is a function that can be defined by evaluating a polynomial.The proofs in geometry help us to solve the various geometric problems.Hope you like the above example of Proofs in geometry.Please leave your comments if you have any doubts.

Ordered Pair

Ordered Pair: an ordered pair is simply a collection of two objects such that one can be distinguished as the first element and the other as the second element, and having the fundamental property that, two ordered pairs are equal if and only if their first elements are equal and their second elements are equal.Formally, an ordered pair with first coordinate a, and second coordinate b, usually denoted by (a, b), is defined as the set {{a}, {a, b}}.Let us see now the meaning of power rule, The power rule for differentiation states that for every natural number n, the derivative of is that is,
Hope you like the above example of Ordered pair and power rule,please leave your comments if you have any doubts.

Introduction to Ellipse

Let us study Ellipse formula,
An ellipse is the locus of a point which moves so that its distance from a fixed point is in a constant ratio, less than one, to its distance from a fixed line.
The fixed point is called the focus of the ellipse. The fixed line is called the directrix of the ellipse. The constant ratio is called the eccentricity of the ellipse and is denoted by e.
Equation of an Ellipse
Let S(h,k) and ax+by+c=0 be the focus and directrix of an elipse respectively. Let e be the eccentricity of the ellipse.
Let P(x,y) be a general point on the ellipse.

I hope the above explanation was useful, now let us study maths symbols

What is Graph Theory

Let us study What is Graph Theory,

Graph Theory:
In learn online representations, the graph theory is used. The selected area shows the isomerism’s common area between graphs and other forms. In spectral graph theory, the graphs can be denoted by algebraic structures.
Order Theory:
In learn online representations, the order theory is also used. From the experiments, each graph is shaped by the intersection of the graphs in an ordered set called as containment or inclusion relation. The containment instructions for a class of normal objects are Boolean pattern of dimensional order n.
I hope the above explanation was useful.

Explain Solution set

Let us study about Solution set,

The set of ordered pairs (x,y), which satisfy the given inequation, is called the solution set of the inequations.
Graphical representation of linear inequations on the real number line

A real number line can be used to represent the solution set of an inequation (Linear).
The convention is that O (a hollow circle) marks the end of a range with a strict inequality (i.e. <>) and (a darkened circle) marks the end of a range involving equality as well as inequality.

Examples:



I hope the above explanation was useful.

What do you call a six sided shape

What do you call a 6 sided shape ?

Hexagon is one of the polygon type. In polygon different shapes contains different sides. Each of the polygon shape is named as different based on the shape and size. One of the six sided shape is the hexagon. Hence, the polygon contains the 6 sided and 6 vertices. Schlafli symbol present in the regular hexagon. The interior angle of any degree is 720 degree. Let we see about many information about hexagon.

Properties of Six Sided Shape Hexagon:

From the above definition we can define many properties.

Property 1: Amount of triangles used in hexagon

Property 2: Amount of diagonal used in the hexagon

Property 3: Total number of the internal angles used in the hexagon shape.

I hope the above explanation was useful.

Arc Length and Arc Length Formula

Arc Length and Arc Length Formula: Arc refers to a part of a circle or a curve. In case of the circle contains the minor arc and major arc. The arc length of minor is the multiplication of circumference of a circle and fraction of an angle (0/360).The length of an arc is called arc length. Radius of a circle and angle (o) can be making a formula of length.The arc length can be either small or large.Let us learn some key points of Arc Length Problems. The length of arc of the circle is given by the central angle divided by 360 degree which is multiplied by the circumference. If the circumference of the circle is given by 2pr then the length of arc of the semicircle is pr.


Let us now look at Arc Length Of Circle Theorem.The given axes be AB and CD .Take the region in Centre e and foci, mark points in any way as you like as shown in the figure.Describe arcs at g, g, g, and g then these points of intersection will be in the curve of the ellipsis upon f and f, with b 1 for radius.In similar way we will find other points. We can find h by taking 2 for one radius and b2 for another radius. By taking b 3 for one radius, and a 3 for the other i is found , always using the foci for centres. Trace the points c, g, h, i, b, etc.,Then we will be getting an ellipse shape as shown in the figure.Hope you like the above example of Arc Length and arc Length Formula.Please leave your comments, if you have any doubts.

Derivatives

Applications of Derivatives Help:Let us understand the concept of application of derivatives help.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.The derivative, measures the rate at which the dependent variable changes with respect to the independent variable.










It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer science.While studying derivatives we are faced with many questions related to application of Derivatives.The degree of a differential equation whose differential coefficients have positive integral powers is defined as the highest power(positive integral index) of the highest order derivative in it.The last but not the least concept which needs attention is application of Derivatives solved probles.We can find many solved problems related to this topic.Hope you like the above example of Derivative.Please leave your comments, if you have any doubts.

Learn Sine Rule

Let us study about sine rule in Trigonometry,

Introduction :

An equation containing the trigonometrical functions of an unknown quantity is termed as a trigonometrical equation, which holds for some values (and not for all values) of the quantities involved.
Co-terminal Angles

The angles (2p + A), (4p + A)......have the same initial and terminal arm as the angle A and so these angles are called co-terminal angles. For all such angles, the value of any trigonometric ratio is the same. Thus, all co-terminal angles are trigonometrically equivalent.

Theorem 1
General solution of sin q = k.

Theorem 2
General solution of cos q = k.

Theorem 3
General solution of tan q = k.

Theorem 4
General solution of acosq + bsinq = c.

I hope the above explanation helped you, now let me explain Cos.

Introduction of coordinate Geometry

Let us learn about coordinate Geometry,

The use of geometry dates back to before the beginning of history. However, it was often used in a very practical manner. It wasn't till about 600 BC that mathematicians began using formal logic and reasoning.

Coordinate plane--a two-dimensional surface on which a coordinate system has been set up; invented by Rene Descartes; also called Cartesian plane, graph, coordinate grid

Coordinates--the numbers in an ordered pair that locate a point in the coordinate plane

Ordered pair--a pair of numbers, written as (x,y), that represents a point on a coordinate grid

Line segment--the part of a line between two points on the line, including the two points

X-axis--the horizontal number line on a coordinate grid

Y-axis--the vertical number line on a coordinate grid

Quadrants, Origin

To plot points, always write the x value first and then the y value.

Ex. (2, 3) (3, -1) (-2, 3) (-3, -2)

Postulates and Theorems

Let us study about postulates and theorems,

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. Listed below are six postulates and the theorems that can be proven from these postulates.

* Postulate 1: A line contains at least two points.

* Postulate 2: A plane contains at least three noncollinear points.

* Postulate 3: Through any two points, there is exactly one line.

* Postulate 4: Through any three noncollinear points, there is exactly one plane.

* Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.

* Postulate 6: If two planes intersect, then their intersection is a line.

* Theorem 1: If two lines intersect, then they intersect in exactly one point.

* Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point.

* Theorem 3: If two lines intersect, then exactly one plane contains both lines.

I hope the above explanation was useful

Comparing Statistical Results

Let us study how to do comparing statistical results,
Making predictions is only one use of statistics. Suppose you have recently developed a new headache/pain remedy that you call Ache-Away. Should you produce Ache-Away in quantity and make it available to the public? That would depend, among other concerns, upon whether Ache-Away is more effective than the old remedy. How can you determine that?

One way might be to administer both remedies to two separate groups of people, collect data on the results, and then statistically analyze that data to determine if Ache-Away is more effective than the old remedy. And what if the results of this test showed Ache-Away to be more effective? How certain can you be that this particular test administration is indicative of all tests of these two remedies? Perhaps the group taking the old remedy (the control group) and the group taking Ache-Away (the treatment group) were so dissimilar that the results were due not to the pain remedies but to the differences between the groups.

It's possible that the results of this test are far off the results that you would get if you tried the test several more times. You certainly do not want to foist a questionable drug upon an unsuspecting public based upon untypical test results. How certain can you be that you can put your faith in the results of your tests? You can see that the problems of comparing headache remedy results can produce headaches of their own.
Hope the above explanation was useful to you.

Inequalities:

Inequalities:

Introduction to inequalities:

In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not.

* The notation a < b means that a is less than b.

* The notation a > b means that a is greater than b.

* The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b".

In contrast to strict inequalities, there are two types of inequality statements that are not strict.

* The notation a ≤ b means that a is less than or equal to b (or, equivalently, not greater than b)

* The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not less than b).

This was a very general view about the meaning of Inequalities,now let us understand the look at a more definite explanation,An inequalities is a statement, that relates the size or order of two objects or about whether they are the same or not.Solving linear inequalities is very much similar to solving linear equations, except for one small but important change: you flip the inequality sign whenever you multiply or divide the inequality by a negative number. In linear equation we don’t do that.

Procedure for Solving Inequalities:


As in the case of solving inequalities equations, there are certain rules for the inequality problems which do not change the solutions. Here is a list of "permissible'' manipulations:

Step1: Adding/subtracting the same number on both sides.

Step2: Switching sides and changing the orientation of the inequality sign.

Step3: Multiplying/dividing by the same positive number on both sides.

Step4: Multiplying/dividing by the same negative number on both sides and changing the orientation of the inequality sign.

* The notation a < b means a is less than b.
* The notation a > b means a is greater than b.
* The notation a ≠ b means a is not equal to b,
* The notation a ≤ b means a is less than or equal to b (or, equivalently, not greater than b)
* The notation a ≥ b means a is greater than or equal to b

Inequalities - Example Problems:

Solving inequalities for Addition and Subtraction:

1. 4x+2 < -2x+14

Solution:

4x+2-2 < -2x+14-2

4x < -2x+12

4x+2x < -2x+2x+12

6x < 12

6x /6< 12/6

x < 2

Hope you like the above example of Inequalities.Please leave your comments, if you have any doubts.

Data Analysis and Interpretation

Data Analysis and Interpretation:
Let us understand how we can analyse the data and interpret it,in this blog let us understand the basic meaning of Data analysis and Interpretation.Next let us understand the meaning of Interpretation,the basic meaning of Interpretation is The power or explaining.
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains.But the statistical data analysis is the data analysis plan to examine the research questions. Statistics, Data Analysis, and Probability introduce statistics as a problem-solving process. Different ways to organize, represent data, describe and analyze variation in data. In this introduction, we will briefly discuss those statistical concepts that provide the necessary foundations for more specialized expertise in any area of statistical data analysis.

Statistical Data Analysis:

To find what statistical data analyses are, first we go to define statistics. Statistics is a group of methods that are used to collect, analyze, present, and interpret data. Statistical data analysis gives hands to promote the use of statistical techniques to apply in order to make decisions in the problem solving in data analysis.

Steps for Statistical Data Applications:

In generally statistical data analysis involves four basic steps:

Step1. Defining the problem is step 1.

Step2. Collecting the data is the step 2.

Step3. Analyzing the data is step 3.

Step4. Reporting the results is last step.

Defining the Problem:

A correct definition of the problem is imperative in order to obtain exact correct data about it. It is very difficult to getting data without clear explanation of the problem.

Collecting data:

When the data are collecting and statistical methods have become easy.

Analyzing the Data:

Statistical data analyses are divides methods for analyzing data into two categories: 1. Eploratory methods, nd 2. Confirmatory methods.

Exploratory methods:

Exploratory methods are used for cover what the data seems to be simple arithmetic and draw pictures to summarize the data.

Confirmatory methods:

Confirmatory methods use ideas from probability theory for answer the specific questions.

Reporting the Results:

Through inferences, an estimate the characteristics of a population can be obtained from a sample. The results may report in the form a graph or a set (or) group of percentages.


Statistical Data Analysis Applications are Given Below:

* Statistical methods are used to help people for identify, study, and solve many complex problems.

* The statistical data analysis is used for so many applications; like that the statistical data analysis section will discuss the assumptions of regression, which include the removing of outliers from the data set, the examining of the linearity, and constant variance.

* The statistical data analysis section should know about how the regression will be interpreted. The statistical data analysis plan should state that the linear regression is being evaluated for the model fit,

* And then it is the part of the statistical data analysis is to discuss the R-square value of the linear regression.

* Then the next part of the statistical data analysis plan would be to examine the beta coefficient, the t-value,

* The last part of the statistical data analysis would discuss the significant beta in terms of the criterion variable happiness

* The statistical data analysis also approximates the sample size needed for the analysis.

Hope you like the above example of Data Analysis and Interpretation.Please leave your comments, if you have any doubts.

Correlation Theory and Regression Analysis

Correlation Theory and Regression Analysis:

The term correlation deals with the relationship between two or more variables. If a change in one variable effect a change in other variable, the variables are said to be correlated.

There are basically three types of correlation, namely,

* Positive correlation
* Negative correlation
* Zero correlation.

In this Blog, let us also learn about Regression.

Regression Definition:

A regression is defined as a statistical analysis assessing the association between two variables. It is used to find the relationship between two variables.


Regression Formula:

Regression Equation(y) = a + bx
Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
Intercept(a) = (ΣY - b(ΣX)) / N

where
x and y are the variables.
b = the slope of the regression line
a = the intercept point of the line and the y axis.
N = Number of values or elements
X = First Score
Y = Second Score
ΣXY = Sum of the product of first and Second Scores
ΣX = Sum of First Scores
ΣY = Sum of Second Scores
ΣX 2 = Sum of square First Scores.

Correlation study are frequently used in psychology research to explain about relationships between the variables. There is a necessary relationship between two variables that can be study about correlation, one variable causes a change in another variable does not proved by finding a correlation relationship. we can study that no equal causation in correlation.

The Purpose of Correlation Study:

Correlation study used for the purpose of representing the relationships between variables. Correlation has three possible way of study: a negative correlation, a positive correlation and no correlation and no correlation. The measurement of correlation co-efficient of correlation strength and the range can be measured from –1 to +1.

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Positive Correlations: Both variables are increase or decrease at the same time. A correlation coefficient nearer to +1 represents a strong positive correlation.
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Negative Correlations: Indicates the increase in the amount of one variable, the other decreases (and vice versa). A correlation coefficient nearer to -1 represents a strong negative correlation.
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No Correlation: It Indicates no relationships between two variables. The correlation coefficient of 0 represents no correlation.

Types of Correlation Study:

1. Naturalistic Observation:

Naturalistic observation explains about recording and observing the number of variables interested in the natural environment without manipulation or interference by the experimenter.

2. The Survey Method:

The most common methods for surveying and questionnaries used in psychological research. In this survey method, the participants can be selected by random sampling can complete a survey, test, or question that is related to variables of interest. Ensuring generalizability of survey results is one of the vital part for random sampling.

3. Archival Research:

Archival research can be performed by the method of analyzing study and this is conducted by researchers of other area or they looking for historical patient records.
Purpose

The correlation is a different way to measure how that is associated with two related variables. The research looks at things that already exist and determines if and in what way those things are related to each other. By doing correlations the purpose is to allow us to make a what we know about one variable based on prediction for another variable.

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Curve Fitting

Curve fitting equation:

Introduction to curve fitting equation:

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data.
The study of ways of constructing functions whose graphs are curves that "best" approximates a given collection of points.We consider approximations by linear functions, polynomials of degree 2 or 3 and exponential functions using the method of least squares. After working through these materials, the student should be able

* to calculate using a graphing calculator or computer software the least squares line, parabola or third degree equation which best fits data.


Curve Fitting Equation:

Built-in curves are able to be use as an assist for data revelation, near assume value of a purpose wherever no data are obtainable; also to go over the associations with two or else further variables. Extrapolation illustrates to the make use of a fixed curve away from the collection of the practical data, with is the topic to a larger degree of indecision given that it might reproduce the way use to make the curve as greatly when it reproduce the experiential data.



Equation for Curve Fitting:

Permit establish through a 1st degree polynomial equation:

y=ax+b

This be a line through slope a. We identify to a line determination attach whichever two points. Thus, a 1st degree polynomial equation is an accurate fit during whichever two points.

Condition we raise the order of the equation toward a next degree polynomial, we obtain:

y=ax2+bx+c

Determination accurately fit an easy curve toward three points.

But we enlarge the order of the equation toward a 3rd degree polynomial, we obtain:

y=ax3+bx2+cx+d

These resolve accurately well four points.

A further common statement would exist toward declare it resolve accurately well four constraints. Every constraint be able to be a point, angle, otherwise curvature. Angle with curving constraints is mainly a lot additional toward the split ends of a curve; also during such belongings be call end conditions.

The curve fit for the polynomial equation is

Y (x) = P(x, n) = a0 + a1*x + a2*x2 ... + ... an*x n

The curve fit for the nonlinear approximation is

F(y) = a0*f0(x) + a1*f1(x) + ... + an*fn (x)

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Standard Probability:

Standard Probability:

Introduction:

A standard probability normal table is also known as “Unit Normal Table" is a numerical table for the values of Φ, the cumulative distribution task of the sharing. They are used to locate the probability that a statistic is practical below, above, or connecting values on the standard normal distribution, and by addition, any normal distribution.Let us now learn about the uses of standard Probability spaces,standard probability spaces are used routinely in ergodic theory, which cannot be said on probability theory. Some probabilists hold the following opinion: only standard probability spaces are pertinent to probability theory, thus, it is a pity that the standardness is not included into the definition of probability space. Others disagree, however:

Arguments against standardness:

* the definition of standardness is technically demanding;
* the same about the theorems based on that definition;
* it is possible (and natural) to build all the probability theory without the standardness;
* events and random variables are essential, while probability spaces are auxiliary and should not be taken too seriously.

Arguments in favour of standardness:

* conditioning is easy and natural on standard probability spaces, otherwise it becomes obscure;
* the same for measure-preserving transformations between probability spaces, group actions on a probability space, etc.;
* ergodic theory uses standard probability spaces routinely and successfully;
* being unable to eliminate these (auxiliary) probability spaces, we should make them as useful as possible.


Normal Distributions:

Normal distributions are symmetrical, bell-figure distributions that are useful in describing actual-earth information. The standard probability normal distribution, represent by the text Z, is the normal distribution has a denote of 0 and a standard deviation of 1. Since probability table cannot be printed for every normal distribution, (there are infinite), it is general practice to change a normal to a standard normal, and use a Z table to find probabilities.

Reading the Table:

Tables use at least 3 different conventions, depending on the understanding of the meaning of an entry such as 1.58:

Cumulative: This is nearly all common, and gives Prob (Z ≤ 1.58)

Complementary cumulative: The complement (1–x) of more than: Prob (Z ≥ 1.58)

Cumulative from zero: The cumulative probability, initial from 0: Prob (0 ≤ Z ≤ 1.58)

These can easily be check by inspect a number like 2.99:

* If this is just about 1 , next it display cumulative probabilities;
* If this is just about 0 , next it display complementary probabilities;
* If this is just about 0.5 , next it display cumulative from 0 probabilities.



Printed tables typically give cumulative probabilities, the possibility that a statistic takes a number less than or the same to a number, from at smallest amount.


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Simplex

Simplex:

Introduction:

Let us understand the meaning of Simplex Method.
The Simplex method is a method which goes from one BFS or extreme point of the feasible region of an Linear programming problem expressed in tableau form to another BFS, in such a way as to continually increase or decrease the value of the objective function until optimality is reached.The simplex method moves from one extreme point to one of its neighboring extreme point.

In geometry,a simplex (plural simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope with n + 1 vertices, of which the simplex is the convex hull. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a pentachoron. A single point may be considered a 0-simplex, and a line segment may be viewed as a 1-simplex.

Definition of a Simplex is given below:

A simplex may be defined as the smallest convex set which contains the given vertices.A regular simplex is a simplex that is also a regular polytope. A regular n-simplex may be constructed from a regular (n − 1)-simplex by connecting a new vertex to all original vertices by the common edge length.

Simplex method Problem 1:

Consider

x1 + x2 - x3 + x4 = 5

2x1 – 3x2 + x3 + x5 = 3

-x1 + 2x2 - x3 + x6 = 1

Solution:

The initial tableau is given by

Tableau 1:

x1 x2 x3 x4 x5 x6 b B1

x4 1 1 -1 1 0 0 5 1 0 0

x5 2 -3 1 0 1 0 3 0 1 0

x6 -1 2 -1 0 0 1 1 0 0 1

The current basic solution is [ 0, 0 , 0, 5, 3, 1]T which is feasible. Suppose we choose a1,1 as our pivot element. Then after one pivot operation, we have

Tableau 2:

x1 x2 x3 x4 x5 x6 b B1

x1 1 1 -1 1 0 0 5 1 0 0

x5 0 -5 3 -2 1 0 -7 2 1 0

x6 0 3 -2 1 0 1 6 -1 0 1

We note that the current basic solution is [ 5, 0, 0, 0, -7, 6]T which is infeasible. Using the new (2, 2) entry as pivot, we have

Tableau 3:

x1 x2 x3 x4 x5 x6 b B1

x1 1 0 -2/5 3/5 1/5 0 18/5 1 0 0

x2 0 1 -3/5 2/5 -1/5 0 7/5 2 -3 0

x6 0 0 -1/5 -1/5 -3/5 1 9/5 -1 2 1

The current basic solution is [ 18/5 , 7/5, 0, 0, 0, 9/5]T and is feasible. Finally, let us eliminate the last slack variable x6 by replacing it by x3.

Tableau 4:

x1 x2 x3 x4 x5 x6 b B1

x1 1 0 0 1 -1 -2 0 1 1 -1

x2 0 1 0 1 -2 -3 -4 2 -3 1

x3 0 0 1 1 -2 -5 -9 -1 2 -1

The current basic solution is [ 0, -4, -9, 0, 0, 0]T which is infeasible and degenerate.

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